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- W4327990576 abstract "Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation. In this paper we transfer this into frequency domain, where the Westervelt equation gets replaced by a coupled system of Helmholtz equations with quadratic nonlinearities. For the case of the to-be-determined nonlinearity coefficient being a characteristic function of an unknown, not necessarily connected domain $D$, we devise and test a reconstruction algorithm based on weighted point source approximations combined with Newton's method. In a more abstract setting, convergence of a regularised Newton type method for this inverse problem is proven by verifying a range invariance condition of the forward operator and establishing injectivity of its linearisation." @default.
- W4327990576 created "2023-03-21" @default.
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- W4327990576 date "2023-03-17" @default.
- W4327990576 modified "2023-10-16" @default.
- W4327990576 title "Nonlinearity parameter imaging in the frequency domain" @default.
- W4327990576 doi "https://doi.org/10.48550/arxiv.2303.09796" @default.
- W4327990576 hasPublicationYear "2023" @default.
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